a. Field of the Invention
The present invention relates to apparatus for measuring birefringence of stressed material automatically, and especially to apparatus capable of making plural measurements of birefringence without requiring the specialized skill of one trained in the art of photoelasticity.
b. Description of the Prior Art
Photoelasticity is the property exhibited by some transparent isotropic solids of becoming doubly refracting when subjected to stress and is used in experimental stress analysis. Since differences of principal stress can be established at every point in transparent solids using photoelasticity techniques, such techniques have become increasingly useful for establishing design criteria, improving product integrity and reliability, verifying designs for structural safety, and reducing product weight and costs.
It is known that the index of refraction (n) for a transparent homogeneous isotropic material, is equal to the speed of light in a vacuum (c) divided by the speed of light in the transparent homogenous isotropic material (v). For such a material the index of refraction is independent of the orientation of any plane of polarized light being transmitted through the transparent material. Although the transparent material, and notably plastics, are isotropic when unstressed, they become anisotropic when subjected to stress or deformation. The index of refraction thus becomes a function of the intensity of stresses applied and the direction of these stresses.
Originally, photoelasticity was employed as a tool for the analysis of flat models being subjected to a plane stress. In this simplified form it provided information on stress concentration factors for typical discontinuities, such as holes, notches, and grooves. Much of this information has been compiled in handbooks and design manuals.
A process of "stress freezing" was developed, in which a three-dimensional model of a structure is: (1) cast or machined utilizing a stress free transparent plastic, (2) heated to its softening point, and (3) finally subjected to forces, pressures and other moments such that upon cooling the completed model the pattern of birefringence and deformation is locked in. A model obtained by stress freezing can be sliced into any number of desired planes and every plane can then be analyzed using photoelasticity so as to provide complete three-dimensional stress analysis of the model.
More recently, techniques for testing the structures have been developed whereby transparent materials (or coatings) are cemented to a structure and surface stresses are measured using a reflection photoelasticity technique.
Several techniques have been employed to measure birefringence. Normally, polariscopes have been employed to effect such measurements by measuring at each point both the direction and magnitude of the difference of principal stresses or strains.
A transmission polariscope is used to analyze transparent models or specimens and is also used for the analysis of sliced planes or three-dimensional models. It has a light source and a polarizer which is positioned on one side of a model or specimen to be analyzed, and an analyzer which is positioned on another side of the model.
A reflection polariscope, which employs the principle of double passage of light, is used mainly for photoelastic coatings, with polarizer and analyzer placed on the same side of the model material.
These polariscopes can either be "plane" or "circular". In each of the two polariscope arrangements, plane and circular, intensity of light transmitted (I) is a function of the relative retardation (.DELTA.) and the orientation of principal stresses (.beta.).
The relations between the transmitted light intensity (I), relative retardation, (.DELTA.) orientations (.beta.) and principal stresses (.delta.1, .delta.2) are well known.
For the plane polariscope: ##EQU1##
For circular polariscope, using crossed polarizers (also called "darkfield"): EQU I=Io sin.sup.2 (.pi..DELTA./.lambda.)
For circular polariscope, using parallel polarizers (also called ("light field"): EQU I=Io cos.sup.2 (.pi..DELTA./.lambda.)
In these expressions:
I and IO is the emerging and entering light intensity. PA1 .lambda. is the wavelength of monochromatic light. PA1 B is the direction of principal stresses. PA1 (1) Full field isochromatic photography, revealing pictorially a complete stress distribution; PA1 (2) Point-per-point use of a Babinet-type compensator; PA1 (3) Point-per-point measurements of fractional orders, using the analyzer rotation; and PA1 (4) Automatic, point-per-point electronic data acquisition systems, using one of the above listed principles. (See U.S. Pat. No. 3,902,805).
The difference of principal stresses (.delta.1-.delta.2) is given by Brewster's law: EQU .delta.1-.delta.2=(.DELTA./tc)
where (t) is the thickness of stressed material and (c) is the material sensitivity.
In the plane polariscope, the intensity of light transmitted becomes zero if the polarizer is parallel to one of the directions of principal stress (.delta.1, .delta.2). This condition is satisfied at several points, normally, and a line or a complete area will appear black. Such a line or an area is called an isoclinic line. At every point on an isoclinic line, the direction of principal stress is either the same as the direction of the polarizer, or perpendicular to it. When the polarizer and analyzer are rotated together, the isoclinic line moves to a new position, thus making it possible to completely explore directions of principal stress throughout the part analyzed.
The circular polariscope is similar to the plane polariscope except that it additionally includes a pair of quarter wave plates. The purpose of the quarter wave plates is to eliminate sensitivity of the polariscope to the direction of principal stresses. In the case of the circular polariscope, where the analyzer is perpendicular to the polarizer (dark field), light intensity becomes zero when the relative retardation is equal to an integral multiple of the wave length of light used (.DELTA.=N.lambda.). If monochromatic light is used, a series of black lines are observed. Along every black line, i.e. isochromatic fringe, the "fringe order" (N) remains constant (N=0, 1, 2, . . . ). Strain and stress fringe values (C.sub..epsilon.,C.sub..EPSILON.) are usually established by calibration. The difference of principal stresses or principal strains can be established at every point once the fringe order (N) is measured.
One of the difficulties in using polariscopes has been the skill required and human evaluation necessary to determine the fringe order (N) both integers and fractions.
In order to accomplish this, a compensator, such as a quartz crystal, or permanently deformed plastic exhibiting a calibrated variable retardation, is introduced according to one technique between the specimen analyzed and the analyzer. The compensator is superimposed so that its principal directions coincide with the directions of principal stresses in the plastic specimen plate. When retardation in the compensator and the measured retardation are numerically equal, but opposite in sign, total intensity observed is zero.
One apparatus, U.S. Pat. No. 3,902,805, addresses the measurements of relative retardation of light waves propagating at different speeds through a stressed material automatically by splitting light waves emerging from the stressed plate or coating into at least two beams, filtering each beam with a filter which transmits a different wave length, transforming the light intensity from each filter into electric signals, and measuring phase shift between those electrical signals resulting from rotation of a polarizer by means of a motor, the difference in phase between the signals is proportional to retardation and the birefringence. The resulting phase difference can be displayed on a voltmeter, or a digital meter, or can be continuously recorded. The above measurement can be accomplished only after the direction of the measured stresses is determined and the quarter wave plate is then placed in alignment with the direction of stress.
From the above discussion it can be seen that the measuring of birefringence (.DELTA./t) has been accomplished by one of the following methods:
In all above methods difficulties arise because before the actual value of the retardation can be established, the direction of stresses must be determined, a proper numerical value must be assigned to each fringe observed, and when the points of interest are not covered by a fringe, a "fractional" order must be measured.